There have been a number of proposals to improve the turning performance of a vehicle by controlling the braking force and/or the traction force individually for the front and rear wheels or for the right and left wheels, and most of them are designed to achieve a desired vehicle handling by detecting a dynamic state of the vehicle body, such as a yaw rate, for a feedback control. However, as long as the vehicle contacts the road surface via tires, the handling of the vehicle is dictated by the dynamic characteristics of the tires. In particular, in the region where the cornering force saturates, it becomes extremely difficult to control the vehicle so as to achieve a desired cornering performance solely on the basis of the dynamic state of the vehicle body.
The inventors therefore previously proposed, in copending U.S. patent application Ser. No. 08/848,498 filed May 8, 1997, a method and system for controlling the handling of a vehicle which achieve a favorable responsiveness and stability even when the dynamic characteristics are outside a linear region. The contents of this copending patent application are hereby incorporated in this application by reference. This technology produces a certain yawing moment which gives rise to a favorable responsiveness to a steering maneuver involving braking (or traction) even in the nonlinear region of the dynamic tire characteristics by controlling the fore-and-aft forces of the tires according to the sliding mode control process (refer to "Sliding Mode Control", published by Corona Publishing Company). The outline of this control process is briefly described in the following.
The basis of this control process consists of basic equations of motion of the vehicle on a two-dimensional plane which take into account the yawing moment around the gravitational center of the vehicle body, and these equations are given in the following. EQU mV(d.beta./dt+.gamma.)=Y.sub.F +Y.sub.R (1)
I(d.gamma./dt)=L.sub.F Y.sub.F -L.sub.R Y.sub.R +M.sub.Z (2)
where
m: vehicle mass PA1 V: vehicle speed PA1 .gamma.: yaw rate PA1 Y.sub.F : front wheel cornering force (sum for right and left wheels) PA1 Y.sub.R : rear wheel cornering force (sum for right and left wheels) PA1 I: yaw moment of inertia PA1 L.sub.F : distance between the front axle and the gravitational center PA1 L.sub.R : distance between the rear axle and the gravitational center PA1 M.sub.Z : yawing moment due to the braking or traction force around the gravitational center (see FIG. 9) PA1 m: vehicle mass PA1 Y.sub.F : front wheel cornering force (sum for right and left wheels) PA1 Y.sub.R : rear wheel cornering force (sum for right and left wheels).
The sliding surface S defining a desired response which is ultimately desired to be achieved can be expressed by the following equation. EQU S=d.beta./dt+c{.beta.+a[(Y.sub.F +Y.sub.R)/mV-.gamma.]}=0 (3)
where c, a and k are appropriately selected constants. The quality of the control process depends on the selection of these constants.
Equation (3) causes the vehicle body slip angle .beta. to converge to zero. The sliding condition for achieving this can be given by the following equation. EQU dS/dt=-kS (4)
From Equations (3) and (4), the following relation can be derived. EQU d.sup.2.beta./dt.sup.2 +c{d.beta./dt+a[(dY.sub.F /dt)/mV+(dY.sub.R /dt)/mV-d.gamma./dt]}+k(d.beta./dt)+kc{.beta.+a[(Y.sub.F +Y.sub.R)/mV-.gamma.]}=0 (5)
If a yawing moment M.sub.Z which satisfies Equation (5) can be obtained in a both reasonable and practical form by using Equations (1) and (2), it can be used a control rule. From Equation (1), one can obtain EQU d.sup.2.beta./dt.sup.2 ={(dY.sub.F /dt)+(dY.sub.R /dt)}/mV-d.gamma./dt (1-2)
When this is substituted into Equation (5), one can obtain EQU (1+ca)[(dY.sub.F /dt)/mV+(dY.sub.R /dt)/mV-d.gamma./dt]+kca[(Y.sub.F +Y.sub.R)/mV-.gamma.]+(k+c)d.beta./dt+kc.beta.=0 (6)
Equation (2) produces EQU d.gamma./dt=(L.sub.F Y.sub.F L.sub.R Y.sub.R +Mz)/I (2-2)
When this is substituted into Equation (6), one can obtain EQU {(dY.sub.F dt)+(dY.sub.R /dt)}/mV-(L.sub.F Y.sub.F -L.sub.R Y.sub.R +Mz)/I+[kca/(1+ca)].multidot.[(Y.sub.R +Y.sub.R)/mV-.gamma.]+(d.beta./dt)[(k+c)/(1+ca)]+.beta.[kc/(1+ca)]=0 (7)
Equation (7) produces the following equation which may serve as a basic control rule. EQU Mz=-(L.sub.F Y.sub.F -L.sub.R Y.sub.R)+(I/mV).multidot.{(dY.sub.F /dt)+(dY.sub.R /dt)}+kca/(1+ca).multidot.I.multidot.[(Y.sub.F +Y.sub.R)/mV-.gamma.]+I(d.beta./dt)[(k+c)/(1+ca)]+I.beta.[kc/(1+ca)] (8)
The above equation means that a yawing moment which achieves a favorable response can be obtained from such parameters as the cornering forces Y.sub.F and Y.sub.R, the yaw rate .gamma., the vehicle speed V, and the vehicle body slip angle .beta.. Since the tread L.sub.TR is fixed, once the yawing moment Mz is given, the right and left ratio of the fore-and-aft forces or the braking (or traction) forces for the final control result can be determined from the following equation. EQU Mz=(X.sub.R -X.sub.L)L.sub.TR (9)
By controlling the fore-and-aft forces individually for the right and left wheels according to a known method (braking force control: Japanese patent laid open publication 7-69190, traction force control: Japanese patent laid open publication 7-17277), it becomes possible to improve the response and stability of the vehicle under conditions where the dynamic properties of the tires exceed the linear range.
In the above mentioned algorithm, it was pre-supposed that at least the frictional coefficient .mu. between the tires and the road surface and the vehicle body slip angle .beta. are known. However, sensors for directly detecting the frictional coefficient between the tires and the road surface and the vehicle body slip angle have not been available in such forms as to be applicable to mass produced vehicles, and it has been customary to estimate the former from the difference in the rotational speeds of the front and rear wheels, and the latter from such readily detectable vehicle state variables as the yaw rate and the lateral acceleration. In other words, according to the prior art, the control accuracy has been strongly dictated by the precision in the values which can only be indirectly estimated.